Mathematical models of neurons with complex dynamics have been derived and numerically simulated on digital computers. See E. Izhikevich, “Which Model to Use for Cortical Spiking Neurons?,” IEEE Trans. on Neural Networks, vol. 15, no. 5, September 2004. However, this work of Izhikevich is limited to deriving mathematical equation models and their numerical simulation in a discrete-time digital computer.
Previously other circuits to implement neurons have been proposed. One example is the circuit of G. Indiveri, see “A low Power Adaptive Integrate-and-Fire Neuron Circuit,” IEEE International Symposium on Circuits and Systems, vol. IV, pp. 820-823, 2003. However the circuit described therein cannot produce the complex biologically-inspired complex behaviors of the mathematical models of Izhikevich.
Other circuits, with similarity to neurons, are time encoder circuits and second order time encoder circuits. See A. A. Lazar and L. T. Toth, “Perfect Recovery and Sensitivity Analysis of Time Encoded Bandlimited Signals,” IEEE Trans. on Circuits and Systems—I, vol. 51, no. 10, pp. 2060-2073, October 2004 which describes a first order neuron circuit and J. Cruz-Albrecht and P. Petre, “Pulse Domain Encoders and Filter Circuits,” U.S. Pat. No. 7,403,144, Jul. 22, 2008 which describes a second order neuron circuit. However the basic time encoder circuits described in these documents also cannot produce complex biologically-inspired neural behaviors, such as those of the mathematical models of Izhikevich.
FIG. 1 shows prior a prior art pulse encoder (see U.S. Pat. No. 7,403,144). This circuit can convert an analog signal into pulses. However this prior art pulse encoder circuit cannot be used to emulate complex neuron behaviors modeled by Izhikevich, for example.
There is a need for circuits that allow the implementation of complex neuron dynamics, such as those modeled by Izhikevich, and preferably with simple analog components. The disclosed circuit can handle the mathematical model of Izhikevich, which can reproduce a large number of biologically inspired neuron behaviors. This mathematical model requires at least two state variables and also a nonlinear element.